Let $a$ be an integer $>0$. By associating with every normal series $(H_i)_{0\leq i\leq n}$ of the group $\mathbb{Z}/a\mathbb{Z}$ the sequence $(s_i)_{1\leq i\leq n}$, where $s_i=[H_{i-1}:H_i]$, a one-to-one correspondence is obtained between the composition series of $\mathbb{Z}/a\mathbb{Z}$ and the finite sequences $(s_i)$ of integers $>0$ such that $a=s_1\ldots s_n$.
What is the codomain of this one-to-one correspondence? Is it $\bigcup_{n\in\mathbb{N_{\geq1}}}\mathbb{N}_{\geq 1}^{[1,n]}$?